Connectivity for an unlabelled bridge-addable graph class
Combinatorics
2020-06-04 v2
Abstract
Let the class A of graphs be bridge-addable; that is, whenever a graph G in A has vertices u and v in different components then the graph G+uv is in A. For a random graph sampled uniformly from the graphs in A on vertex set {1,..,n}, there are known lower bounds on the probability of being connected (for example, the probability is always at least 1/e). We ask here about similar results when the random graph is sampled uniformly from the unlabelled n-vertex graphs in A.
Keywords
Cite
@article{arxiv.2001.05256,
title = {Connectivity for an unlabelled bridge-addable graph class},
author = {Colin McDiarmid},
journal= {arXiv preprint arXiv:2001.05256},
year = {2020}
}
Comments
4 pages, open problem presented at the First Armenian Workshop on Graphs, Combinatorics, Probability in May 2019. The second version includes Theorem 5, which gives a lower bound 1/2n on the probability of being connected for unlabelled graphs (and some new references)